$ extit{Ab initio}$ mismatched interface theory of graphene on $alpha$-RuCl$_3$: doping and magnetism.

Recent developments in twisted bilayer graphene revealed a rich phase space of mismatched van der Waals systems and generated excitement. Expanding the scope to hetero-bilayers can offer new opportunities to control van der Waals systems with strong in-plane correlations such as spin-orbit assisted Mott insulator $alpha$-RuCl$_3$. Nevertheless, a theoretical $textit{ab initio}$ framework for mismatched hetero-bilayers without even approximate periodicity is sorely lacking. We propose a general strategy for calculating electronic properties of such systems, Mismatched INterface Theory (MINT), and apply it to a graphene/$alpha$-RuCl$_{3}$ (g/$alpha$-RuCl$_{3}$) heterostructure. Using MINT, we predict uniform doping of 4.7$%$ from graphene to $alpha$-RuCl$_3$ and magnetic interactions in $alpha$-RuCl$_3$ to shift the system towards the Kitaev point. Hence we demonstrate that MINT can guide targeted materialization of desired model systems and discuss recent experiments on g/$alpha$-RuCl$_{3}$ heterostructures.